Hierarchical Elastic Network Modeling of cryo-EM Data

Abstract

Cryo-EM images of molecules are increasing in resolution, extending their uses from rigid-body docking to generation of atomistic density maps independent of prior structural information. Single molecule cryo-EM provides images of a molecule from many viewpoints, which are averaged and compiled to form a 3D reconstruction. This reconstruction determines the smallest possible hull enclosing the molecule, but sacrifices information about dynamic properties of the molecule intrinsically contained in the varied image set.We suggest projecting the images into 3D space, without averaging out inconsistent densities, to form a probability map for the reconstruction. This map contains flexibility information neglected by earlier analyses of dynamics from density maps. To highlight different levels of molecular flexibility found in this map, we use a hierarchical elastic network model (hENM). The hENM uses the Markov transition probabilities between the voxels in the density map to segment the map into sets of multi-resolution nodes. Each voxel is initially taken as a node in the network, after-which the network is iteratively reduced to increasingly coarser sets of important nodes, forming a hierarchy. This method provides a unifying framework in allowing the derivation of dynamics concurrently with the study of information propagation through the network, with segmentation of the protein into structural sub-regions as an additional benefit. As these nodes highlight the core structural regions of the protein, they can also be used as anchor points for fitting high-resolution structures into EM maps. Preliminary results show excellent overlap between the dynamics computed using a Gaussian Network Model of the C-alpha atoms of proteins and those computed from our hENM nodes, validating the role of hENM in predicting intrinsic protein motions. With the greater goal of inferring function from dynamics, we work here to predict dynamics directly from cryo-EM images.